Publication Details:
Journal or Publication Title:
Armenian Journal of Mathematics=Հայկական մաթեմատիկական հանդես
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Title:
Saturation of finitely-generated submodules of free modules over Prüfer domains
Creator:
Faten, Ben Amor ; Ihsen, Yengui
Contributor(s):
Գլխ. խմբ.՝ Անրի Ներսեսյան ; Պատ. խմբ.՝ Լինդա Խաչատրյան ; Խմբ. տեղակալ՝ Ռաֆայել Բարխուդարյան
Subject:
Uncontrolled Keywords:
Valuation domains ; Abelian groups ; Saturation ; Echelon form ; Prüfer domains
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Abstract:
We propose to give an algorithm for computing the $R$-saturation of a finitely-generated submodule of a free module $E$ over a Prüfer domain $R$. To do this, we start with the local case, that is, the case where $R$ is a valuation domain. After that, we consider the global case ($R$ is a Prüfer domain) using the dynamical method. The proposed algorithm is based on an algorithm given by Ducos, Monceur and Yengui in the case $E=R[X]^m$ which is reformulated here in a more general setting in order to reach a wider audience. The last section is devoted to the case where $R$ is a Bézout domain. Particular attention is paid to the case where $R$ is a principal ideal domain ($Z$ as the main example).
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General note:
Electronic Open Access Publication of the National Academy of Sciences of Armenia